s2w4 Precalc FC Laws of sine and cosine

Last updated 8 months ago

29 questions

1

3

1

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s2w4 Precalc FC Laws of sine and cosine

Last updated 8 months ago

29 questions

1

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

1

Lets review congruent vs similar triangles - what is the difference?

1

ok, up until know, trig has been all about the right triangles. But we are about to push a little beyond that. This is called the law of sines

for ANY triangle, where A is the side opposite angle a, B is the side opposite angle b, and C is the side opposite angle C. Given this triangle with sides a, b and c, drag A B and C to their proper angles.

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

1

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

1

Questions 23 & 22

02:15

Question 24

01:34

3

Solve the triangle using Law of Sines.

a=_______ , b=_______ , C=_______ °
you will want to solve for angle C first, and round the lengths to the hundreth place. note that C should be in degrees.

1

solve the triangle using law of cosines
a = 6, b=10, c=11
A=_______ °, B=_______ °, C=_______ °
round to the nearest hundreth, 

1

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

1

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Is the following an identity?

yes

no

Lets review congruent vs similar triangles - what is the difference?

Lets review congruent triangles: you know two triangles are congruent if

you have any two sides and an angle, or any two angle and a side, or all three sides

You have at least two sides and one angle or a side and know it is a right triangle

Any two angles and a side, all three sides, or two sides and the angle between those two sides

you have to know all three sides and one angle

The angles of a triangle add up to

90

180

270

360

ok, up until know, trig has been all about the right triangles. But we are about to push a little beyond that. This is called the law of sines

for ANY triangle, where A is the side opposite angle a, B is the side opposite angle b, and C is the side opposite angle C. Given this triangle with sides a, b and c, drag A B and C to their proper angles.

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

1

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

1

At what angle would the radius of circle B only touch that initial line once?

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

Given the following information about a triangle, which law can you use to find all the other sides?

Side, angle, side
Angle, side, angle
angle, angle, side
side, side, angle
side, side, side
angle, angle, angle

Law of sines
Law of cosines
this does not describe just one triangle

Questions 23 & 22

02:15

Question 24

01:34

Solve the triangle using Law of Sines.

a=_______ , b=_______ , C=_______ °
you will want to solve for angle C first, and round the lengths to the hundreth place. note that C should be in degrees.

solve the triangle using law of cosines
a = 6, b=10, c=11
A=_______ °, B=_______ °, C=_______ °
round to the nearest hundreth, 

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

watching the proofs helps me understand the laws

true

false

categorize

what the law of sines is
what the law of cosines is
when to use the law of sines
when to use the law of cosines
how to simplify or rearrange trig expressions using the identities I know
when are triangles congruent
why SSA gives an ambiguous case
how to use the law of sin to find the area of triangle

ive got this
im fuzzy
so confused

Is the following an identity?

yes

no

Lets review congruent triangles: you know two triangles are congruent if

you have any two sides and an angle, or any two angle and a side, or all three sides

You have at least two sides and one angle or a side and know it is a right triangle

Any two angles and a side, all three sides, or two sides and the angle between those two sides

you have to know all three sides and one angle

The angles of a triangle add up to

90

180

270

360

These two triangles are congruent by

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

two sides and one angle

one angle, one side, and one line where an unknown part of that line is our side

two sides and two angles

two lines, and angle between them and a dot that must be where the last side of the triangle will go.

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

0

1

2

infinite

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

Given the following information about a triangle, which law can you use to find all the other sides?

Side, angle, side

Angle, side, angle

angle, angle, side

side, side, angle

side, side, side

angle, angle, angle

Law of sines

Law of cosines

this does not describe just one triangle

this looks a little like the odd and even function thing - whats the connection?

I don't remember the intersecting chord theorem. Do you?

uh, obviously...

no...

to be honest, that one is just as obscure as all the rest of this geometry I thought was long in my past. 

watching the proofs helps me understand the laws

true

false

categorize

what the law of sines is

what the law of cosines is

when to use the law of sines

when to use the law of cosines

how to simplify or rearrange trig expressions using the identities I know

when are triangles congruent

why SSA gives an ambiguous case

how to use the law of sin to find the area of triangle

ive got this

im fuzzy

so confused

These two triangles are congruent by

S-S-S

S-A-S

A-S-A

A-A-S

none of these

These two triangles are congruent by

S-S-S

S-A-S

A-S-A

A-A-S

none of these

These two triangles are congruent by

S-S-S

S-A-S

A-S-A

A-A-S

none of these

These two triangles are congruent by

S-S-S

S-A-S

A-S-A

A-A-S

none of these

These two triangles are congruent by

S-S-S

S-A-S

A-S-A

A-A-S

none of these

These two triangles are congruent by

S-S-S

S-A-S

A-S-A

A-A-S

none of these

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

two sides and one angle

one angle, one side, and one line where an unknown part of that line is our side

two sides and two angles

two lines, and angle between them and a dot that must be where the last side of the triangle will go.

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

0

1

2

infinite

I don't remember the intersecting chord theorem. Do you?

uh, obviously...

no...

to be honest, that one is just as obscure as all the rest of this geometry I thought was long in my past. 

s2w4 Precalc FC Laws of sine and cosine

s2w4 Precalc FC Laws of sine and cosine

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Lets review congruent vs similar triangles - what is the difference?

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

you'll notice this is the same relationship as the SSA triangle that the sin law didn't help with a couple questions ago. Is there a relationship between cos a and cos (180-a)?

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Is the following an identity?

Lets review congruent vs similar triangles - what is the difference?

Lets review congruent triangles: you know two triangles are congruent if

The angles of a triangle add up to

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

Given the following information about a triangle, which law can you use to find all the other sides?

you'll notice this is the same relationship as the SSA triangle that the sin law didn't help with a couple questions ago. Is there a relationship between cos a and cos (180-a)?

this looks a little like the odd and even function thing - whats the connection?

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

watching the proofs helps me understand the laws

categorize

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

this looks a little like the odd and even function thing - whats the connection?

I don't remember the intersecting chord theorem. Do you?

s2w4 Precalc FC Laws of sine and cosine

s2w4 Precalc FC Laws of sine and cosine

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Lets review congruent vs similar triangles - what is the difference?

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

There is also a law of cosines. it is SIGNIFICANTLY uglierwhere c is the angle opposite B. you might want to pause now and go practice law of sines in aleks homework and the modules.

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

one of the reasons to use identities is so you can rewrite an equation so that there is only one trig function involved. rewrite this equation so that is is only one trig function

Is the following an identity?

Lets review congruent vs similar triangles - what is the difference?

Lets review congruent triangles: you know two triangles are congruent if

The angles of a triangle add up to

Name the two triangles in my diagram that have a 31.9° angle, and two sides, 4 and 6 units long

setting up Law of Sine's here, I getANDWhat do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

There is also a law of cosines. it is SIGNIFICANTLY uglierwhere c is the angle opposite B. you might want to pause now and go practice law of sines in aleks homework and the modules.

Given the following information about a triangle, which law can you use to find all the other sides?

draw the triangle described above. to find the area of the triangle, you need to find the height, how can you do that?

watching the proofs helps me understand the laws

categorize

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

These two triangles are congruent by

Lets go over why SSA is the "ambiguous case" You will see at the top of this image a line. there is a line segment connected to this line at 31.9°, and the line segment is length 0. So far we do not have a triangle, but we do have

I know the second side i want is 4, so to construct my 31.9°, 6,4 triangle, I draw a circle of radius four around my point B. How many times does that circle touch my line?

setting up Law of Sine's here, I getANDWhat do you think the relationship is between angle BCD and angle BDA is?

At what angle would the radius of circle B only touch that initial line once?

this looks a little like the odd and even function thing - whats the connection?

I don't remember the intersecting chord theorem. Do you?

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?

There is also a law of cosines. it is SIGNIFICANTLY uglier

where c is the angle opposite B.
you might want to pause now and go practice law of sines in aleks homework and the modules.

setting up Law of Sine's here, I get
AND

What do you think the relationship is between angle BCD and angle BDA is?